My cat is a very special boy and there's no other cat like him. Does that count?

Polar Bear on the Hudson Bay coast in northern Ontario.

I'm Indigenous and I've gone hunting and trapping with my relatives a few times in my life. On one of those trips we happened on a polar bear on the mud flats of the bay during the late autumn. We drove by in our freighter canoe (a very large oversized canoe with a 60 HP outboard motor) and the bear swam near us and then walked by a few hundred feet away. It wasn't afraid but we were. We watched for a while and then fired rifle shot into the mud next to it to scare it away. From the moment it started to run to the point it disappeared as a speck on the horizon was about a minute or two. I went up later to look at the prints and the clay mud looked like a tractor had driven over it. I couldn't believe how fast it could move on the mud. I quickly sank in my boots and could barely walk around.

One paw print was about the size of my head. I never left camp without someone nearby or a rifle in my hands.

Probably a Takahē in New Zealand but in captivity.

I petted and fed hay to the last male northern white rhino in Kenya some years ago.

He's dead now and the remaining two females will likely die without giving birth and the species will go extinct :-(

Probably Hercules the Liger. Terrifyingly enormous animal--pictures do not do justice to how intimidating a predator of that mass is.

A dik-dik. It's a species of deer that is slightly larger than a house cat or maybe a medium size dog. It was super adorable but a bit uncanny feeling lol.

Uhh, in the wild? I've seen some pretty uncommon wetland birds a number of times. Some pretty weird bugs too, although it's hard to say what they were.

I've seen big moose really up close, and that was epic, and would have been terrifying if there wasn't usually a car-stopping amount of wood between us. They're not rare, though, just shy.

I traveled to one of the most remote places on the planet, drove hours on dirt roads, hiked another hour through deafening wind, and then crawled on my stomach to the edge of a a 1300' cliff, and hung off of it it just to take a picture of a puffin with my cell phone.

In captivity: probably red wolves, or some critically endangered birds at the National Aviary.

In the wild: probably some plants endemic to Catalina Island.

I got a brief but good look at a wild Jaguarundi in south Texas nearly twenty years ago. I thought it was a bobcat at first, but it turned so I could see its tail and profile, and there was no mistaking it.

A live cow

A wild beaver like a few miles from my house, and not a nutria, a real life flat-tailed beaver toothed fucking beaver. I was going to an artificial dam I use as a fishing spot and there he was. It was way bigger than I thought but I didn't want to disturb it so I turned around and went home.

In captivity? An Okapi? A rhino? Idk man I've been to many zoos and exotic zoos where you drive through and idk about the rarest.

Giant Panda and Red Panda maybe.

California condor at Big Sur

I visited a lab where some of the last remaining dusky gopher frogs are cared for.

(reminder that frogs may be in what is considered the sixth mass extinction ever on earth)

There was a stray firefly at my house one night. Like, singular. We're not even near their habitat, so I don't know what's up with that.

https://en.wikipedia.org/wiki/Santa_Cruz_long-toed_salamander

So rare I don't even know if they still exist.

I did some field biology work back in the mid 2000s and this is the only reason I know this.

There is also the California Condor and a species of kangaroo rat in the Mojave. The former is less rare now due to an immense amount of work we did to save the species to the point where they actually got removed from the endangered list at one point.

Look at this little guy though

As for the Condors:

The condor population (wild and captive) has steadily increased, reaching over 460 in 2017 (with 170 wild condors in California). For the most current update check out the Condor Population Status Summary (PDF)

Back when I was doing field work they were down to only 27 and all had been moved to captivity.

The situation with the salamander is much more dire

Its limited range and fragile specialized habitat place severe restrictions to the viability of this species. There is no definitive population estimate for the Santa Cruz long-toed salamander, but the numbers are deemed to be quite small. Further disturbance of its limited habitat could lead to this species' extinction.

Wolverine.

A quetzal in the rainforest of Panama.

Panay monitor lizard.

My buddy was trapping monitor lizards for us to eat and we caught one of those. He recognized it and told me that they were endangered.

We did NOT eat it. It went back into the forest, unharmed.

I saw a numbat at the zoo. Very rare, almost extinct, pretty skittish so even if you do go to their exhibit they're often hiding from everyone

Well that need the disclaimers of "outside a zoo" and "of which i was aware of", but probably Hummingbird hawk-moth, it might not be very rare, but i was like "wtf a hummingbird in Poland?" and i managed to get close enough to see it's in fact a moth.

In the wild: Florida scrub jay. key deer. carracarra. Indigo racer. I don't know how to determine what is rarest. There are a lot I have seen.

Tarsier

Outside of a zoo, maybe American Avocet or Painted Bunting

Saw a fishercat in an industrial area not far from a large swath of floodplain and high voltage transmission lines. So there was a lot of territory for it nearby. Looks like a tall badger. Apparently pretty rare. Was walking around 18 wheeler trucks in motion like it owned the place, peeking around the dumpsters most likely looking for the young raccoons that hang around.

I saw a lynx cat in th3 backyard of a place I was staying at in Washington it was very cool.

A panda at Singapore zoo.

Either a black stork, a least weasel (actually pretty common, but difficult auf to see around here), Cerambyx cerdo (probably not as rare as most regulating bodies think), a Eurasian eagle owl (rare around Germany) or felis silvestris

I was quite lucky to see an i'iwi when I went to Kaua'i Hawai'i. Unfortunately only a couple hundred left because of avian malaria.

Your dad